In general, crosstalk noise arises from any gate that unintentionally affects qubits that should not be involved and should thus remain mere spectators. Operational crosstalk in optically-manipulated trapped-ion systems stems from imperfect addressing, such that light intended to be addressed to a specific set of active qubits also illuminates some spectator qubits, which are the qubits
arranged in the immediate neighbourhood of the active qubits. The origin of this imperfect addressing is generally given by the finite size of the laser focusing spot at the position of the ions. In this work, we consider two different models for crosstalk errors in the MS gate: the entangling crosstalk model and the Stark-shift crosstalk model. It should be noted that whereas single-qubit gates also generate crosstalk, this noise can be greatly suppressed by techniques such as composite sequences [1]} or dynamical decoupling [2]} (see Appendix  for a further discussion). The qubit measurement can also lead to crosstalk, as the measurement process also leads to the scattering of photons from the measured ions, which can subsequently interact with the remaining spectator ions in the string. We note that it is possible to prevent this type of crosstalk by applying spectroscopic decoupling pulses to nearby spectator ions [3]}, such that the scattered photons become off-resonant and the crosstalk is minimised (see Appendix  REF ). Therefore, in the following, we will only focus on crosstalk in MS-gates.
